Author | Ebeling, Wolfgang. author |
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Title | Lattices and Codes [electronic resource] : A Course Partially Based on Lectures by F. Hirzebruch / by Wolfgang Ebeling |
Imprint | Wiesbaden : Vieweg+Teubner Verlag, 1994 |
Connect to | http://dx.doi.org/10.1007/978-3-322-96879-1 |
Descript | XVI, 178 p. online resource |
1 Lattices and Codes -- 1.1 Lattices -- 1.2 Codes -- 1.3 From Codes to Lattices -- 1.4 Root Lattices -- 1.5 Highest Root and Weyl Vector -- 2 Theta Functions and Weight Enumerators -- 2.1 The Theta Function of a Lattice -- 2.2 Modular Forms -- 2.3 The Poisson Summation Formula -- 2.4 Theta Functions as Modular Forms -- 2.5 The Eisenstein Series -- 2.6 The Algebra of Modular Forms -- 2.7 The Weight Enumerator of a Code -- 2.8 The Golay Code and the Leech Lattice -- 2.9 The MacWilliams Identity and Gleasonโs Theorem -- 2.10 Quadratic Residue Codes -- 3 Even Unimodular Lattices -- 3.1 Theta Functions with Spherical Coefficients -- 3.2 Root Systems in Even Unimodular Lattices -- 3.3 Overlattices and Codes -- 3.4 The Classification of Even Unimodular Lattices of Dimension 24 -- 4 The Leech Lattice -- 4.1 The Uniqueness of the Leech Lattice -- 4.2 The Sphere Covering Determined by the Leech Lattice -- 4.3 Twenty-Three Constructions of the Leech Lattice -- 4.4 Embedding the Leech Lattice in a Hyperbolic Lattice -- 5 Lattices over Integers of Number Fields and Self-Dual Codes -- 5.1 Lattices over Integers of Cyclotomic Fields -- 5.2 Construction of Lattices from Codes over